Find the value of $3 a - 2 b$ using the equations $5 b = 6 a + 16$ and $9 a = 7 b - 20$ .

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Solution

The correct option is C $- 4$
$\Rightarrow 5 b = 6 a + 16 \Rightarrow 6 a - 5 b = - 16$ ................(1)
$\Rightarrow 9 a = 7 b - 20 \Rightarrow 9 a - 7 b = - 20$ ................(2)
Multiply the (1) by $7$ and (2) by $5$ , we get
$\Rightarrow 42 a - 35 b = - 112$ ...........(3)
$\Rightarrow 45 a - 35 b = - 100$ .........(4)
Substract (3) and (4), we get
$\Rightarrow - 3 a = - 12$
$\Rightarrow a = \frac{- 12}{- 3} = 4$
Substitute the value of $a$ in (1), we get
$\Rightarrow 6 \times 4 - 5 b = - 16$
$\Rightarrow 24 - 5 b = - 16$
$\Rightarrow - 5 b = - 16 - 24$
$\Rightarrow - 5 b = - 40$
$\Rightarrow b = \frac{40}{5} = 8$
Then the value of $3 a - 2 b = 3 \times 4 - 8 \times 2$
$\Rightarrow 12 - 16 = - 4$

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